The viscoelastic rheology of transient diffusion creep

Polycrystalline materials have a viscoelastic rheology where the strains produced by stresses depend on the timescale of deformation. Energy can be stored elastically within grain interiors and dissipated by a variety of different mechanisms. One such dissipation mechanism is diffusionally-accommodated/-assisted grain boundary sliding, also known as transient diffusion creep. Here we detail a simple reference model of transient diffusion creep, based on finite element calculations with simple grain shapes: a regular hexagon in 2D and a tetrakaidecadedron in 3D. The linear viscoelastic behaviour of the finite element models can be well described by a parameterised extended Burgers model, which behaves as a Maxwell model at low frequencies and as an Andrade model at high frequencies. The parametrisation has a specific relaxation strength, Andrade exponent and Andrade time. The Andrade exponent depends only on the angles at which grains meet at triple junctions, and can be related to the exponents of stress singularities that occur at triple junctions in purely elastic models without diffusion. A comparison with laboratory experiments shows that the simple models here provide a lower bound on the observed attenuation. However, there are also clearly additional dissipative processes occurring in laboratory experiments that are not described by these simple models.